Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
Question
Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
Solution
To solve this problem, we can use the formula for the length of a common chord between two intersecting circles. The formula is:
Length of common chord = 2 * sqrt[(r1^2 - d^2) + (r2^2 - d^2)]
where r1 and r2 are the radii of the two circles and d is the distance between their centres.
Step 1: Substitute the given values into the formula.
Length of common chord = 2 * sqrt[(5^2 - 4^2) + (3^2 - 4^2)]
Step 2: Simplify the equation.
Length of common chord = 2 * sqrt[(25 - 16) + (9 - 16)]
Step 3: Continue simplifying.
Length of common chord = 2 * sqrt[9 + (-7)]
Step 4: Simplify further.
Length of common chord = 2 * sqrt[2]
Step 5: Calculate the square root of 2 (approximately 1.41).
Length of common chord = 2 * 1.41
Step 6: Multiply to find the final answer.
Length of common chord = 2.82 cm
So, the length of the common chord is approximately 2.82 cm.
Similar Questions
Find the length of the common chord of two circles of radii 15 cm and 20 cm, whose centers are 25 cm apart.Choices:- 24 cm 25 cm 15 cm 20 cm
Two equal circles of radius r intersect such that each passes through the centre of the other. The length of common chord of the circles is
Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm and 7 cm. Find the radii of the circles.
The length of a chord which is at a distance of 6 cm from the centre of a circle of radius 10 cm isA 8 cm B 16 cm C 12 cm D 20 cm
Given a circle of radius 5cm and centre O. OM is drawn perpendicular to the chord XY. If OM = 3cm, then length of chordXY is
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.